Statisitics
Judith and Francine, both age 19, have decided to go on a Caribbean cruise, and
they want to have an enjoyable time, which means that they want to travel with
other people their own age. They buy tickets for a cruise where the average age of
the other passengers is 20 years. Can you imagine their surprise at the start of the
cruise when they discover that all the other passengers are parents (average age 32)
with children (average age 8)?

Statistics: the branch of mathematics that deals with collecting, organizing,
displaying, and analyzing.
statistic: a number that describes one aspect of a group of data.
EXAMPLE: mean, median, mode, range, standard deviation, etc...
datum: one bit (piece) of information.
data: many bits (pieces) of information.
Types of Data
quantitative data: data that is numeric
(eg. height, weight, time..)
There are two kinds of quantitative data: continuous and discrete
continuous data: can be represented using real numbers (eg. height, weight,
time, etc..)
discrete data: can be represented by using ONLY intergers (eg. # of people, #
of cars, # of animals, etc..)
qualitative data: data that is non-numeric (eg. colours, flavours, etc...)

Measures of Central Tendency
mean: ( A.K.A. 'the arithmetic mean") the symbol for mean is "x bar". The arithmetic average
of a set of values.
where (x bar) is the mean
where Σx means the sum of all data (x) in the set (Σ is called "sigma")
where n is the number of data in a set
EXAMPLE: find the average mark this set of 5 quizzes: 48,52,65,45,65.

Measures of Central Tendency
median (med): 1) the middle value in an ordered (from smallest to largest) set of data.
2) if there are an even number of data, the median is the average of the
middle pair in an ordered set of data.
EXAMPLE: find the median of these quiz scores: 12,10,17,11,15
SOLUTION: 10, 11, 12, 15, 17
12 is the median.
EXAMPLE: find the median of these scores: 12,10,17,11,15,11
SOLUTION: 10,11,11,12,15,17
the median is 11.5
mode (mo): the datum that occures most frequently in a set of data.
EXAMPLE: find the mode in the set of quiz scores: 12,10,17,11,15,11
SOLUTION: the mode is 11 because it occurs more often that any other number in the set.

Mean, Median, Mode, ...
A clerk in a men's clothing store keeps a weekly record of the number of pairs of
pants sold. The following is her list for two weeks.
Mon Tue Wed Thur Fri Sat
Week1 34 40 36 36 38 38
Week 2 32 36 36 42 34 34
Calculate the mean, mode, and median for the data shown. Click on the correct term
to check your answer.
Bimodal Distribution

Probability of the number
of girls in a family of four.
Theoretical Binomial
(Probability) Distribution
Experimental Binomial
(Probability) Distribution
No data between
0 and 1.
Probabilities of outcomes
when rolling a six sided die.
Uniform (Probability)
Distribution

Type of Distributions...
Uniform Distribution: date may be discrete or continous. Every outcome in
the experiment is equally likely.
Example: graph the distribution that shows what can happen when a 6-sided
die is thrown.
Normal Distributions: Data is continous (height, weight, time, etc.) when
certain experiments are carried out many, many, many times the probability
graph of the data tend to be "bell shaped" this is known as the "Normal Curve."
Binomial Distribution: data is discrete (# of heads when ten coins are tossed,
# of spades in a 13 card hand , etc.). When a binomial experiment is conducted
many, many, many times a portion of the related histogram approches the
shape of the normal curve.